A justifiable attitude, and quite parallel to the development of the 'third
protocol' that defines the Red Crystal - but consider, as I suggested in my
reply to Ken, that it was Sylea, not Vland or Terra, that was the center of
the nascent Third Imperium (and thus not unlikely to impose their own
symbology, just as a fast answer to "we need some sort of consistent
symbology for this").
I think symbology, once established, is likely to be _highly_ conserved Consider:
* the various astrological/alchemical symbols are still used as short-hand on astronomical charts;
* religious/political symbols (the cross in all its variations, the Roman eagle, yin-yang);
* mathematical functions; and even
* musical notation.
(For simplicity, from this point forward, I will use the term 'the "Red" Cross' to refer to the shape of the Red Cross - with arms of equal length to their width - without any reference to the colour. I think the _shape_, which is not legally protected in the way the red-on-white or white-on-red versions of that shape are protected, is a universally recognised symbol, and is likely to be for a long, long time.)
In as much as new symbology is developed, it is to meet the needs of new universal concepts arising (reload, on/off, home, save ... just looking around my computer screen). I have having a hard time thinking of examples where a widely recognised symbol for a concept which continued to be important was replaced by another "new" symbol. A case in point is the stubborn persistence of the 3.5" floppy as the save icon (despite many attempts to replace it with more generic symbols), and the old rotary-dial handset (or whole phone) to represent the phone function ... and these _clearly_ outdated icons do not have the weight of generations of use behind them!
Against that high degree of conservation, I see the Rule of Man starting out using well-established Terran standard icons. (And I think, your current concerns aside Jeff, this would almost certainly include the Red - or colourblind - Cross.) Within a century or two, there would be a "survival of the fittest" between the Terran icons and their Vilani equivalents - probably with the simplest (or most unambiguous - just imagine the "Red" Cross being the Vilani universal symbol for toilet facilities) winning.
By the time of Twilight some 3-400 years later, there would be a new universal standard for icons throughout the Imperium. This standard would be the standard used by the Sylean Protectorate and all its successor states through until the Third Imperium. At its nadir, the Sylea continued to control 4 subsectors (GURPS Humaniti). I cannot see any cultural crises during that nadir which trigger a wholesale replacement of the fused Vilani/Terran symbology for a newly developed "Sylean" iconography.
I DO like your integration of the red crystal, the ankh, and the "Red" Cross. Perhaps even throw in the upward "T" and you have the fusion symbol that might come out of Vilani and Terran ambiguities. Imagine an upside-down 5-pointed asterisk (
https://tinyurl.com/robz44u)
with the upper two arms coming together to make a "Red" Crystal.
So, looking for a backstory ...
Early leaders of the Rule of Man see the Vilani "upward T" (looking like the image I sent, but with a longer stem) and think - "Hmm, looks too much like an up arrow to most Terrans. They see the Terran-official Red Cross and think - "Nope, that's the Vilani toilet symbol ... and besides, we need something that is colour independent."
A graphic designer comes up with the "outreaching ankh" (as described above). To Vilani, it can be sold as better than the Red Cross as it incorporates the Vilani "upward-T". Across Terran-dominated space, the Red Cross and Crescent are gradually replaced with the Red Crystal on the various international and national organisations that use those icons, and the Crystal (heedless of colour) occupies the same place in our shared iconography that the "Red" Cross does today. When Terrans see the "outreaching ankh" they notice the Crystal at its head; more literary-minded Terrans might also recognise the ankh-symbol too. Both the Crystal and the ankh identify the "outreaching ankh" as the universal symbol for health care. Even many minor races might see the symbol as a generic upright sophont, and get achieve buy-in that way.
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Cheers,
Ken